Quantization is usually the wish to make a transition from classical physics to quantum physics. While not being of any physical interest (the world is already quantum!) it reflects the problem that it is rather easy to understand mathematical models for classical systems but much more difficult to construct directly models for the quantum world. Here quantization enters as a mathematic approach to find such quantum descriptions. There is no widely accepted and mathematically sound definition of quantization available, but many competing theories of quantization. Them most prominent techniques are geometric quantization, deformation quantization and star products, path integral quantization and many more. Quantization is also closely related to a real physical problem which is sort of inverse to it: the understanding of the classical limit of quantum systems.
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